About Optics & Photonics TopicsOSA Publishing developed the Optics and Photonics Topics to help organize its diverse content more accurately by topic area. This topic browser contains over 2400 terms and is organized in a three-level hierarchy. Read more.

Topics can be refined further in the search results. The Topic facet will reveal the high-level topics associated with the articles returned in the search results.

Abstract

The detective quantum efficiency for foveal vision is computed from the flash perception data of Blackwell and McCready. The detective quantum efficiency is identical with the concept of quantum efficiency introduced by Rose in 1946, and is defined as the square of the ratio of the smallest possible threshold to the observed threshold, where the smallest possible threshold is set by the statistical fluctuations in the number of the background photons entering the eye. The computed values of the detective quantum efficiency Q are tabulated in Table V, and depend on the target diameter α, on the light pulse duration T, and on the background luminance B. The maximum values of Q (with the respect to variation of α and T) range from about 0.25% to about 1.0 %over the range from 0.1 to 100 ft-L, with the maximum value occurring at about 1.0 ft-L. The computed values of Q are free of the questionable assumptions previously used by Rose and by Jones regarding integration time and threshold signal-to-noise ratio.

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Table I

The entries are the values of the signal-to-noise ratio k required by an ideal detector to achieve a reliability q and a false alarm fraction f.

False alarm fraction f

Signal-to-noise ratio k

q =50%

q =90%

q =99%

50%

0.67

1.64

2.58

10%

1.41

2.62

3.65

1%

2.34

3.62

4.66

0.1%

3.09

4.37

5.42

0.01%

3.72

5.00

6.05

Table II

The entries are the values of the signal-to-noise ratio k required by an ideal detector to achieve a reliability q in an M-channel forced-choice situation.

Reliability q

Signal-to-noise ratio k

M = 2

M = 4

M = 8

50%

0.95

1.22

1.52

90%

2.36

2.65

2.93

99%

3.25

3.80

4.11

Table III

The entries are the values of threshold contract C (for a reliability q = 50% in a four-channel forced-choice situation) with a target diameter α in minutes and a background luminance B in ft-L. All of the entries are for a light pulse duration of 0.1 sec. The values of C greater than 0.5 are in parentheses.

α

B = 100

10

1

0.1

0.01

0.001

1

0.3459

(0.5808)

(1.380)

(5.808)

(42.56)

(413.0)

2

0.08650

0.1452

0.3451

(1.452)

(10.64)

(103.3)

4

0.02624

0.04217

0.09772

0.3972

(2.911)

(28.31)

10

0.01462

0.01977

0.03802

0.1291

(0.9462)

(9.204)

20

0.01164

0.01489

0.02535

0.07413

(0.5432)

(5.272)

60

0.009376

0.01140

0.01637

0.03917

0.2871

(2.793)

Table IV

Pupil diameters and Stiles-Crawford factors.

B ft-L

D mm

S

D2S mm2

100

2.8

0.93

7.3

10

4.0

0.84

13.4

1

5.0

0.76

19.0

0.1

6.1

0.66

24.5

0.01

7.0

0.58

28.6

0.001

7.4

0.55

30.0

Table V

This is the chief table of this report, and contains the main results. The entries in the table show the detective quantum efficiency Q in percent for the target diameter α (in angular min) in the first column, for the target duration T (in seconds) shown at the head of the column, and for the luminance B indicated above that section of the table. The entries that are derived from a contrast C greater than 0.5 are placed in parentheses.

α

B = 100 ft-L

T = 1/1000

T = 1/309

T = 1/100

T = 1/30

T = 1/10

T = 1/3

T = 1

1

(0.000764)

(0.00247)

(0.00764)

(0.0184)

0.0234

0.0159

0.0110

2

(0.00306)

(0.00988)

0.0306

0.0735

0.0935

0.0637

0.0442

4

(0.00818)

0.0265

0.0818

0.197

0.254

0.166

0.106

10

(0.00480)

0.0155

0.0480

0.119

0.131

0.0762

0.0376

20

(0.00225)

0.00729

0.0225

0.0550

0.0516

0.0276

0.0112

60

0.000523

0.00169

0.00523

0.0109

0.00885

0.00419

0.00140

B = 10 ft-L

1

(0.00138)

(0.00446)

(0.0126)

(0.0293)

(0.0452)

0.0462

0.0279

2

(0.00551)

(0.0178)

(0.0503)

0.117

0.181

0.185

0.112

4

(0.0169)

(0.0546)

0.154

0.362

0.536

0.481

0.292

10

(0.0158)

0.0512

0.144

0.328

0.390

0.237

0.125

20

(0.00894)

0.0289

0.0815

0.176

0.172

0.0896

0.0412

60

0.00240

0.00778

0.0219

0.0447

0.0326

0.0152

0.00551

B = 1.0 ft-L

1

(0.00102)

(0.00329)

(0.0102)

(0.0276)

(0.0564)

(0.0612)

(0.0350)

2

(0.00407)

(0.0132)

(0.0407)

(0.110)

0.226

0.246

0.139

4

(0.0131)

(0.0424)

(0.131)

0.354

0.704

0.756

0.424

10

(0.0166)

(0.0536)

0.166

0.427

0.744

0.690

0.334

20

(0.0115)

0.0371

0.115

0.278

0.418

0.342

0.155

60

(0.00409)

0.0132

0.0409

0.0943

0.112

0.0718

0.0248

B = 0.1 ft-L

1

(0.000314)

(0.00102)

(0.00314)

(0.0108)

(0.0247)

(0.0293)

(0.0148)

2

(0.00126)

(0.00407)

(0.0126)

(0.0433)

(0.0989)

(0.117)

(0.0590)

4

(0.00428)

(0.0138)

(0.0428)

(0.137)

0.330

0.370

0.187

10

(0.00666)

(0.0215)

(0.0666)

0.221

0.500

0.417

0.190

20

(0.00493)

(0.0160)

(0.0493)

0.166

0.379

0.233

0.0993

60

(0.00203)

(0.00626)

0.0203

0.0661

0.151

0.0602

0.0238

Table VI

The maximum values of the detective quantum efficiency Q for each of four background luminances, and also the target diameters α and the pulse durations T for which the maximum is achieved.

B ft-L

0 %

α min

T sec

100

0.255

4.4

0.09

10

0.575

5.5

0.15

1.0

0.92

6.0

0.18

0.1

0.525

8.5

0.15

Tables (6)

Table I

The entries are the values of the signal-to-noise ratio k required by an ideal detector to achieve a reliability q and a false alarm fraction f.

False alarm fraction f

Signal-to-noise ratio k

q =50%

q =90%

q =99%

50%

0.67

1.64

2.58

10%

1.41

2.62

3.65

1%

2.34

3.62

4.66

0.1%

3.09

4.37

5.42

0.01%

3.72

5.00

6.05

Table II

The entries are the values of the signal-to-noise ratio k required by an ideal detector to achieve a reliability q in an M-channel forced-choice situation.

Reliability q

Signal-to-noise ratio k

M = 2

M = 4

M = 8

50%

0.95

1.22

1.52

90%

2.36

2.65

2.93

99%

3.25

3.80

4.11

Table III

The entries are the values of threshold contract C (for a reliability q = 50% in a four-channel forced-choice situation) with a target diameter α in minutes and a background luminance B in ft-L. All of the entries are for a light pulse duration of 0.1 sec. The values of C greater than 0.5 are in parentheses.

α

B = 100

10

1

0.1

0.01

0.001

1

0.3459

(0.5808)

(1.380)

(5.808)

(42.56)

(413.0)

2

0.08650

0.1452

0.3451

(1.452)

(10.64)

(103.3)

4

0.02624

0.04217

0.09772

0.3972

(2.911)

(28.31)

10

0.01462

0.01977

0.03802

0.1291

(0.9462)

(9.204)

20

0.01164

0.01489

0.02535

0.07413

(0.5432)

(5.272)

60

0.009376

0.01140

0.01637

0.03917

0.2871

(2.793)

Table IV

Pupil diameters and Stiles-Crawford factors.

B ft-L

D mm

S

D2S mm2

100

2.8

0.93

7.3

10

4.0

0.84

13.4

1

5.0

0.76

19.0

0.1

6.1

0.66

24.5

0.01

7.0

0.58

28.6

0.001

7.4

0.55

30.0

Table V

This is the chief table of this report, and contains the main results. The entries in the table show the detective quantum efficiency Q in percent for the target diameter α (in angular min) in the first column, for the target duration T (in seconds) shown at the head of the column, and for the luminance B indicated above that section of the table. The entries that are derived from a contrast C greater than 0.5 are placed in parentheses.

α

B = 100 ft-L

T = 1/1000

T = 1/309

T = 1/100

T = 1/30

T = 1/10

T = 1/3

T = 1

1

(0.000764)

(0.00247)

(0.00764)

(0.0184)

0.0234

0.0159

0.0110

2

(0.00306)

(0.00988)

0.0306

0.0735

0.0935

0.0637

0.0442

4

(0.00818)

0.0265

0.0818

0.197

0.254

0.166

0.106

10

(0.00480)

0.0155

0.0480

0.119

0.131

0.0762

0.0376

20

(0.00225)

0.00729

0.0225

0.0550

0.0516

0.0276

0.0112

60

0.000523

0.00169

0.00523

0.0109

0.00885

0.00419

0.00140

B = 10 ft-L

1

(0.00138)

(0.00446)

(0.0126)

(0.0293)

(0.0452)

0.0462

0.0279

2

(0.00551)

(0.0178)

(0.0503)

0.117

0.181

0.185

0.112

4

(0.0169)

(0.0546)

0.154

0.362

0.536

0.481

0.292

10

(0.0158)

0.0512

0.144

0.328

0.390

0.237

0.125

20

(0.00894)

0.0289

0.0815

0.176

0.172

0.0896

0.0412

60

0.00240

0.00778

0.0219

0.0447

0.0326

0.0152

0.00551

B = 1.0 ft-L

1

(0.00102)

(0.00329)

(0.0102)

(0.0276)

(0.0564)

(0.0612)

(0.0350)

2

(0.00407)

(0.0132)

(0.0407)

(0.110)

0.226

0.246

0.139

4

(0.0131)

(0.0424)

(0.131)

0.354

0.704

0.756

0.424

10

(0.0166)

(0.0536)

0.166

0.427

0.744

0.690

0.334

20

(0.0115)

0.0371

0.115

0.278

0.418

0.342

0.155

60

(0.00409)

0.0132

0.0409

0.0943

0.112

0.0718

0.0248

B = 0.1 ft-L

1

(0.000314)

(0.00102)

(0.00314)

(0.0108)

(0.0247)

(0.0293)

(0.0148)

2

(0.00126)

(0.00407)

(0.0126)

(0.0433)

(0.0989)

(0.117)

(0.0590)

4

(0.00428)

(0.0138)

(0.0428)

(0.137)

0.330

0.370

0.187

10

(0.00666)

(0.0215)

(0.0666)

0.221

0.500

0.417

0.190

20

(0.00493)

(0.0160)

(0.0493)

0.166

0.379

0.233

0.0993

60

(0.00203)

(0.00626)

0.0203

0.0661

0.151

0.0602

0.0238

Table VI

The maximum values of the detective quantum efficiency Q for each of four background luminances, and also the target diameters α and the pulse durations T for which the maximum is achieved.